Sculptures are often used to set a mood or define the character of particular area. For example, theme sculptures are often used as a center of focus in parks, building plazas, atriums and similar locations. Each such sculpture is normally generated by an artist for a particular situation, and the artist's concept of the desired mood or theme may be quite different from that which is perceived by the sponsor or owner of the work. Thus, a sponsor may be disappointed in a work or feel that his input has been ignored.
The present invention provides a sculpture and a means for designing a sculpture that provides a logical nexus between a theme and a sculpture. This nexus is accomplished by generating a sculpture from a seed structure, and the seed may be selected to embody the desired theme. For example, a sculpture designed for the plaza of an office tower may use the shape of the tower as a seed from which a sculpture is generated. Since the seed or parts thereof remain as a portion of the sculpture, the theme of the seed (such as the tower) is necessarily carried forward in the sculpture. In such case, the sponsor of a sculpture and the casual observer will be able to recognize the theme of the seed, such as a tower, that is continued and amplified in the sculpture. As more fully described below, however, the artist remains free to choose the precise manner of expression of the sculpture within certain confines of the present method.
In accordance with the present invention, a method is disclosed for producing a sculpture that has three component types, namely, a seed, edge extensions or rods, and an adjoint surface. First, a seed is defined in the form of any polyhedron which for present purposes may be defined as a three dimensional volume bounded by algebraically defined surfaces. That is, the surfaces of the seed are defined by algebraic equations.
Next, rods are formed along edge extensions of the seed. The edge extensions are defined by the seed and, more particularly, are defined by the edges of the seed. Since the surfaces that bound the seed are defined algebraically, the surfaces will intersect along edges which are also defined by algebraic equations. To determine the position of the rods, the algebraic equations that define the edges are used to extend the edges beyond the seed and, thus, define rod positions (edge extensions) extending in space from the seed. Some of these edge extensions may be infinite in length and the artist must terminate the rods that extend along the edge extensions at a selected length. In other cases, the edge extensions will be a closed configuration such as a circle or an ellipse. In such case, the artist, if he chooses, may provide rods that extend for the entire distance of the edge extensions.
Finally, an adjoint surface is defined and modeled in space. The adjoint surface is defined by the seed and the edge extensions. One might expect, that with space being so large, it would be rare for the aforementioned edge extensions to intersect in space, but, in fact, the edge extensions do intersect except in certain degenerate cases such as a cubic or conical seed. In the non-degenerative cases, the intersection points of the edge extensions define a unique surface that is generated by an algebraic equation having a maximal order of M-4 where M is defined as the sum of the orders of the surfaces of the seed. For example, assume a seed is bounded by five surfaces, three of which are defined by equations having an order of one and two of which are defined by equations having an order of two. In such case, the seed would have an order of seven (1+1+1+2+2) and M would be equal to seven. For such seed, the intersecting points would define a unique adjoint surface which is defined by an equation having a maximal order of M-4 which would be three. This unique adjoint surface would include all of the intersection points and all of the points in the adjoint surface may be determined by solving the aforementioned equation having an order of three.
Thus, in summary, the sculpture is formed by defining and forming a seed in space, positioning rods extending outwardly from the seed along edge extensions and forming an adjoint surface portion which is disposed on an adjoint surface that is defined by the edge extension intersection points and an algebraic equation having a maximal order of M-4. In the preferred embodiment, the seed and the adjoint surface are connected together by rods extending along the edge extensions of the seed.